How To Interact with an Unrooted Android Whose Screen Is Broken (Completely Black & Unresponsive)?

I know this isn't a Turbo-specific issue, but I put this thread here first, in case anybody in here has any ideas that are specific to the Turbo (v1).

For a number of reasons, I also know that I'm probably sunk on this one (so, not completely naive, and not expecting magic), but I'm just checking to see if it's somehow possible.

My Turbo's screen broke, and it is already getting replaced. So, I'm all good as far as that part goes, but...

After it got broken, for a while, I was still able to interact with most of the screen, but the very top half inch was totally black, and completely unresponsive to touch.

Eventually, the 'blackness' kept creeping downward on the screen, and I had to get more and more tricky about how I got to it.
For a while, I was able to see well enough to click on some things, scroll around, etc, and since I was familiar with it, even if I couldn't completely see every icon on the homescreen (can we just call it the desktop at some point? lol ), I was able to guess fairly well. Lists became increasingly difficult.

Early-on, I was able to get in and click the TeamViewer QuickSupport icon and get into it that way (including being able to click on the remote connection confirmation, etc).

At one point, I connected a mouse to the USB port via OTG adapter. Together with TeamViewer, that worked very well.

Well, eventually, the BLACK spread all the way down to the bottom and now completely covers the whole thing, and I am not able to do anything on it, because, TBH, even though I recall generally what's there, I have no idea how far apart things are well enough to click in the correct places to get TeamViewer QuickSupport up and running.

I assume one might ask, "Why didn't you just leave it running so you wouldn't need to get TV going every time?"
My answer = I don't have a good, well-defined, legitimate excuse....I just #$%^&*-up.

Another piece of darkness.....it's not rooted lol

Is there any chance of getting TV or anything else stood up and active so I can get in remotely without being able to directly interact with it by touch?

Oh, by the way, the main thing I still have left that I was needing to do (again, "Why didn't you do that first?"...I know) is to export all of my profiles, etc from Tasker. Any way of getting at them remotely or via USB tools?

p.s. If there's a good, safe root process that can be run completely blind, please let me know. I can only imagine the range of potential solutions would have to be broader if it's rooted.

EDIT: Also, I am searching the forums and reading to see if I can find ideas too....not just being lazy.
Perhaps MyPhoneExplorer (I've used it, but it was a long time ago on my Bionic)?

ALSO: I have the new, replacement v1 Turbo. So, if there's any way of somehow using that in the mix, cool. I assume it can't be opened without hurting it though. So...

MORE: I just recalled that I have a system set up to automatically upload screenshots to my web space. So, I am going to see if I am able to do that. If so, I'm still up against the fact that, I still won't know where the mouse cursor is. I guess I could just take screenshot to find out where it is, move it again, screenshot, move again, and do it like that until I get the mouse where I need to click. Hmmm....I will give this a try, and report back...

...OK, the screenshot auto-uploads are still firing. So, I'm able to see the screen now. I will give the mouse thing a try...

UPDATE:
* the screenshot-auto-upload trick is helping, some
* I'm also able to connect it directly to my PC to get to the internal storage card

However, since I did not yet export all of my data from Tasker, there's nothing to grab from 0\Tasker\Profiles or anything like that.
Any ideas how to accomplish the same thing as what happens when ya do an export in Tasker?